In Long Term Evolution (LTE), user equipment (UE) periodically or aperiodically feedbacks channel state information (CSI) to a network node, e.g., enhanced or evolved NodeB (eNodeB or eNB), of a wireless network. The CSI includes among other things rank indicator (RI), precoding matrix index (PMI) and channel quality indicator (CQI). For PMI and CQI, two types of feedback, namely wideband report and subband report, are supported. For wideband report, all of the resource elements (REs) in the system bandwidth in one subframe can be used to generate the report. For the subband report, the REs in the specified bandwidth in a subframe only can be used. The Physical Layer procedures of the Standard is set forth in the document 3GPP, “LTE Physical Layer Procedures,” ETSI TS 136 213, V8.7.0, June 2009.
The calculation of the CQI is conditioned on the current transmission mode and the best choice of the RI and PMI for the current channel. A straightforward way of selecting RI and PMI is to jointly estimate the two so that the optimum performance metrics is achieved. The joint estimation is normally done by iterating all the possible RIs and all the corresponding precoding matrices in the codebook and selecting the best pair of RI and PMI that yields the optimum metrics. See e.g., Texas Instruments, “Further Details on Codebook-Based Pre-coding for E-UTRA,” 3GPP TSG RAN WG1 #47bis, January 2007, R1-070270. The two commonly used metrics are Mean-Square-Error (MSE), or equivalently Signal-to-Interference Plus Noise Ratio (SINR) and Mutual Information (MI, or capacity), and they do not appear to make any difference in performance. See e.g., Texas Instruments, “Further Details on Codebook-Based Pre-coding for E-UTRA,” 3GPP TSG RAN WG1 #47bis, January 2007, R1-070270; S. Schwarz, M. Wrulich and M. Rupp, “Mutual Information based Calculation of the Precoding Matrix Indicator for 3GPP UMTS/LTE”, International ITG Workshop on Smart Antennas, February 2010 (hereinafter “Schwarz”); D. J. Love and R. W. Heath, Jr., “Limited Feedback Unitary Precoding for Spatial Multiplexing System,” IEEE Trans. IT-51, No. 8, 2005; Ericsson, “System-level evaluation of OFDM—further considerations,” 3GPP TSG RAN WG1 #35, November 2003, R1031303. The MSE-based metrics require the calculation of matrix inversion, and the MI-based metrics require the calculation of matrix determinant. In either case, the metrics and hence the matrix operation is carried out on each and every selected resource element (RE) in the bandwidth of a subframe and the final metrics is the mean of those calculated on all the selected REs. It was noted in Schwarz that the computation effort can be prohibitively large if the number of REs becomes large, e.g., in the case of large system bandwidth and wideband report. Accordingly, Schwarz proposed the idea of combining a subset of REs into one RE. The combination is done by averaging channels of the REs in the subset and using the mean channel matrix to calculate a single metrics for the subset. However, due to the time and frequency varying nature of the channel, the size of the subset must be small to reduce the performance loss caused by the channel averaging and therefore complexity reduction of this approach can be very limited.